Answer to Question #277379 in Microeconomics for lisa

Question

There are 300 identical firms in a perfectly competitive market, the price of the output is p, the short-run cost function of a typical firm in the market is as follows:

 C(q)=q³ - 2q² + 2q+ 10

1. What is this firm’s (short run) average variable cost function?
2. What is this firm’s (short-run) supply function?
3. If p = 17, what is this firm’s maximum profit?
4. If p = 17, what is this firm’s producer surplus?
5. What is the short-run market supply function?
6. If the market demand function is D = 500- 50 √3p-2, what is the short-run market equilibrium price and market equilibrium output quantity?
7. What is the output level and the profit of a typical firm at the market equilibrium from (g)?

Answer 1

Solution:

1.). Average variable cost function = Variable costs/Quantity = q³ - 2q² + 2q /q = q² – 2q + 2

 

2.). Short-run supply function is the same as the MC:

Derive MC:

MC = $\frac{\partial TC} {\partial q}$ = 3q² – 4q + 2

Short-run supply function: q = p $\div$ 3q² – 4q + 2

 

3.). Firms maximum profit:

Profit = TR – TC

q = 8

TR = 17 x 8 = 136

TC = q³ - 2q² + 2q+ 10 = 8² – 2(8²)  + 2(8) + 10 = 64 – 128 +16 + 10 = -38

Maximum profit = 136 – (-38) = 174

 

4.). Producer surplus = ½ x (50 – 17) x 8 = 132

 

5.). Short run market supply function: q = 100/3q² – 4q + 2

 

6.). At equilibrium: Qd = Qs

500- 50 √3p-2 = 100/3q² – 4q + 2

Q = 6

P = 12